text: At the end of the 1960s J. R. Black developed an empirical model to estimate the MTTF (mean time to failure) of a wire, taking electromigration into consideration. Since then, the formula has gained popularity in the semiconductor industry:
  Here  is a constant based on the cross-sectional area of the interconnect,  is the current density,  is the activation energy (e.g. 0.7 eV for grain boundary diffusion in aluminum),  is the Boltzmann constant,  is the temperature in kelvins, and  a scaling factor (usually set to 2 according to Black). The temperature of the conductor appears in the exponent, i.e. it strongly affects the MTTF of the interconnect. For an interconnect of a given construction to remain reliable as the temperature rises, the current density within the conductor must be reduced. However, as interconnect technology advances at the nanometer scale, the validity of Black's equation becomes increasingly questionable.